Details

analyze712.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	74.9%	25.1%	8
6.2%	68.6%	25.1%	9
7.8%	67.1%	25.1%	10
10.1%	64.7%	25.1%	11
14.8%	47.6%	37.6%	12
15.8%	36.8%	47.4%	13
16.6%	35.1%	48.3%	14

sample52.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
11.0ms	197×	body	80	invalid
9.0ms	129×	body	80	nan

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4911	16
1	4911	16

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.3b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 t))
0.0b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
14×	`associate-r_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64`
7×	`sqrt-prod_binary64`
6×	`pow1_binary64` `unpow-prod-down_binary64` `associate-*l/_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `sqrt-pow1_binary64`
3×	`add-log-exp_binary64` `exp-prod_binary64`
2×	`pow-to-exp_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64`

Counts

3 → 66

Calls

3 calls:

2.0ms	(sqrt.f64 (exp.f64 t))
13.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
10.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

series78.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt.f64 (exp.f64 t))
59.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 z 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
16.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2)))

simplify60.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5004	915

prune67.0ms

Filtered

53 candidates to 75 candidates (-41.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	8	76

Merged error: 0.0b

Counts

76 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 t))
0.0b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.2b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.4b	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log_binary64`
22×	`associate-r_binary64` `prod-exp_binary64`
20×	`add-cbrt-cube_binary64`
19×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`sqrt-prod_binary64`
12×	`pow1_binary64` `associate-*l/_binary64`
10×	`cbrt-unprod_binary64`
6×	`unpow-prod-down_binary64`
5×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `sqrt-pow1_binary64`
3×	`pow-to-exp_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `exp-prod_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`pow1/2_binary64` `sqr-pow_binary64` `rem-sqrt-square_binary64`

Counts

4 → 96

Calls

4 calls:

2.0ms	(sqrt.f64 (exp.f64 t))
15.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
8.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
11.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))

series98.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt.f64 (exp.f64 t))
63.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
12.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
20.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 2))

simplify59.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4969	1323
1	4969	1323

prune72.0ms

Filtered

70 candidates to 108 candidates (-54.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	108	8	116

Merged error: 0.0b

Counts

116 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.2b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

105×	`add-exp-log_binary64`
79×	`prod-exp_binary64`
41×	`cbrt-unprod_binary64`
39×	`add-cbrt-cube_binary64`
36×	`pow1_binary64`
26×	`associate-r_binary64`
22×	`pow-prod-down_binary64`
20×	`associate-*l/_binary64`
17×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`sqrt-prod_binary64`
6×	`pow-to-exp_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `cbrt-prod_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`sqr-pow_binary64`

Counts

4 → 128

Calls

4 calls:

25.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
8.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
19.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
17.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

series144.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
12.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
18.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
47.0ms	(.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

simplify70.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4959	2094
1	4959	2094

prune90.0ms

Filtered

74 candidates to 140 candidates (-89.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	139	9	148

Merged error: 0b

Counts

148 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
0.2b	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
0.3b	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
40×	`prod-exp_binary64`
34×	`associate-r_binary64` `add-cbrt-cube_binary64`
25×	`sqrt-prod_binary64`
20×	`pow1_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64` `associate-*l/_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow-prod-down_binary64`
6×	`associate-l_binary64` `unpow-prod-down_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`sqr-pow_binary64`

Counts

4 → 116

Calls

4 calls:

24.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
8.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
12.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
17.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(.f64 (.f64 (.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
12.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z))
20.0ms	(.f64 (.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2)))
19.0ms	(.f64 (.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

simplify64.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4968	1793
1	4968	1793

prune71.0ms

Filtered

75 candidates to 128 candidates (-70.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	3	5
Picked	0	1	1
Done	1	2	3
Total	129	8	137

Merged error: 0b

Counts

137 → 8

regimes511.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	16
1	29	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

464.0ms	8000×	body	80	valid
347.0ms	6070×	body	80	invalid
251.0ms	4503×	body	80	nan

Details

analyze712.0ms

sample52.0ms

simplify118.0ms

prune7.0ms

localize12.0ms

rewrite29.0ms

series78.0ms

simplify60.0ms

prune67.0ms

localize13.0ms

rewrite40.0ms

series98.0ms

simplify59.0ms

prune72.0ms

localize16.0ms

rewrite76.0ms

series144.0ms

simplify70.0ms

prune90.0ms

localize15.0ms

rewrite66.0ms

series121.0ms

simplify64.0ms

prune71.0ms

regimes511.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling